I think the Constitution needs to just accept that the states aren't equal and they never have been.
Abolish the Senate, and replace it with something similar to what the House of Lords is in the UK.
A (noble) upper house with little actual power.
Most of the Senate's powers, like ratifying treaties could go to the House of Representatives.
Presidential appointments would be automatic, with the House of Representatives being able to impeach and convict appointees, but not having the ability to vote on the nomination of said appointees.
Interestingly a number of (insignificant) UK politicians have proposed doing the reverse. Richard Leonard for example wanted to replace the House of Lords with a 'Senate of nations and regions.' I would imagine that would be elected more like the UK's former European Parliament delegation though.
I wonder how you would want the membership of this house to be elected/appointed, and why that is at all preferable to simply having a unicameral legislature.
